Intelligent energy and thermal comfort management in

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Intelligent energy and thermal comfort management in grid-connected microgrids with heterogeneous occupancy schedule

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Christos D. Korkasb,c,∗, Simone Baldia,c , Iakovos Michailidisb,c , Elias B. Kosmatopoulosb,c

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Delft Center for Systems and Control, Delft University of Technology, Delft 2628CD, The Netherlands Dept. of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi 67100, Greece Informatics & Telematics Institute, Center for Research and Technology Hellas (ITI-CERTH), Thessaloniki 57001, Greece b

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Abstract Energy efficient operation of microgrids, a localized grouping of controllable loads with distributed energy resources like solar photovoltaic panels, requires the development of energy management systems (EMSs) with the capability of controlling the loads so as to optimize the aggregate performance of the microgrid. In microgrids comprising of buildings of different nature (residential, commercial, industrial, etc.), where the occupants exhibit heterogeneous occupancy schedules, the objective of an effective management strategy is to optimize the aggregate performance by intelligently exploiting the occupancy schedules and the intermittent production of solar energy. This paper presents a simulation-based optimization approach for the design of an EMS in grid-connected photovoltaic-equipped microgrids with heterogeneous occupancy schedule. The microgrid exchanges energy, buying or selling it, with the main grid and the EMS optimizes an aggregate multi-objective criterion that takes into account both the energy cost and the thermal comfort of the occupants of the microgrid. Simulative results obtained using a microgrid test case developed in EnergyPlus demonstrate the effectiveness of the proposed approach: the proposed EMS strategy is shown to take advantage of the occupancy information, intelligently and automatically changing the energy demand of each building according to the occupants’ behavior, and achieving relevant improvements with respect to alternative EMS strategies.

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Keywords: Occupancy-based zone-climate control, Energy efficiency, Thermal comfort, Energy management system, Grid-connected microgrids

∗ Corresponding

author. Tel.: +30 2541 551597 Email addresses: [email protected] (Christos D. Korkas ), [email protected] (Simone Baldi), [email protected] (Iakovos Michailidis), [email protected] (Elias B. Kosmatopoulos) Preprint submitted to Applied Energy

June 15, 2015

Nomenclature and symbols:

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BEPS: CCU: DER: DMS: EMS: HJB: HVAC: MG: PCAO: PPD: PV: RBC: PCRBC: RES:

Building Energy Performance Simulation Central Control Unit Distributed Energy Resource Demand Side Management Energy Management System Hamilton-Jacobi-Bellman Heating, Ventilation, and Air Conditioning Microgrid Parameterized Cognitive Adaptive Optimization Predicted Percentage of Dissatisfied people Photovoltaic Rule Based Controller Pre-Cooling Rule Based Controller Renewable Energy Source

i pBi pSi EiPV Qi Fi fc fp ESi CSi k sp f dt

(subscript) referring to building # i Buying energy cost of building # i [A C/kW h] Selling energy cost of building # i [A C/kW h] Available PV energy for building # i [kW h] Energy required by building # i [kW h] Thermal comfort for building # i [%] scaling factor of comfort scaling factor of pricing (scaled) Energy score of building # i (scaled) Thermal comfort score of building # i weighting factor for energy/comfort trade-off HVAC set point [oC] fan speed [%] energy management sample time [s]

1. Introduction Nowadays, energy crisis is one of the most compelling problems that society must face. According to studies from the U.S. Department of Energy and the European Commission Directorate-General for Energy, nearly 40% of the total energy consumption in developed countries is attributable to buildings [34, 6, 8, 16]. Improving efficiency in industrial, commercial and residential energy consumption is thus a crucial challenge to be addressed. The transition from a conventional power grid to a smart grid which integrates measurements, communication and control technologies, is identified as a necessity with a view to energy efficiency [24]: in a smart grid scenario, a promising framework to break away from massive centralized energy production is the Microgrid (MG) concept, where a localized grouping of controllable loads uses Distributed Energy Resources (DERs) to satisfy its energetic needs [41, 23, 7]. A microgrid can either operate in islanded mode or be grid-connected: in the second case the MG operates in parallel with the 2

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main grid and it can buy and sell energy. The energy efficient operation of MGs requires the development of an appropriate Energy Management System (EMS), that manages all the controllable loads in the microgrid so as to optimize the aggregate performance of the system. In MGs comprising of buildings of different nature (residential, industrial, commercial, etc), greater improvements can be achieved if the EMS collects information from all these buildings and make them work cooperatively to improve the performance of the whole system. Due to the fact that buildings of different nature exhibit different occupancy patterns, i.e. the occupancy schedule of the MG is heterogeneous, the energy demand of each building must be managed without violating the thermal comfort of occupants. The occupancy schedule is a particularly delicate factor in microgrid optimization, since the behaviour of the occupants affects the energy demand in a complex manner. Energy efficiency buildings can be improved by changing the indoor climate in response to occupancy change: the importance of occupancy information in joint optimization of energy consumption and thermal comfort has been recognized in several studies focusing on single smart buildings [40, 29, 14, 42]. The extension of intelligent occupancy-based control for joint energy efficiency and thermal comfort in microgrids require the development of an effective EMS with the capability to intelligently shape the energy demand and to integrate the DERs taking into account the occupancy schedule of each building. In this work we study an energy management strategy which minimizes both the energy cost and thermal discomfort in grid-connected photovoltaic-equipped microgrids with heterogeneous occupancy schedule. 1.1. Related work The optimization of the operations in MGs is attracting the interest of many researchers, and several approaches and problem formulations have been proposed in the literature: model predictive control has been adopted in [30] to achieve economic efficiency in microgrid operation management: in [43] an interactive strategy aims at integrating commercial buildings into smart grid; in [37] simulated-annealing maximizes the financial gain of a grid-connected MG, while in [25] a gravitational search algorithm is used in an islanded microgrid. The optimization of the balance between power generation and load demand in MGs with different DERs has also been taken into account in many studies: optimization based on multi-agent systems has been proposed for the demand side management of polygeneration microgrids [21], while [27, 26] propose experimental validations of real-time EMS in islanded microgrids. A decision-making perspective has also been adopted in optimizing operations in MGs: in [35] a decision-making optimization tool named Distributed Energy Resources Costumer Adoption Model (DER-CAM) optimizes energy cost and CO2 emissions by taking strategic decisions on building shell improvements and DER investments; [18] develops a mathematical programming framework for the operational planning of residential-scale microgeneration systems. The literature on microgrid optimization is vast and the one presented is not an exhaustive list. To the best of the authors’ knowledge, however, thermal comfort, with a few exceptions [12], is often neglected in EMS for optimization of MG operations. Thermal comfort plays an important role since it expresses the user satisfaction with respect to the thermal state: furthermore, thermal comfort defines a trade-off with energy cost, since, generally speaking, extra energy is required in order to keep the users more satisfied. The energy cost/thermal comfort optimization is challenging because it is subjected not only to the building dynamics, which are typically uncertain, but also to the intermittent nature of renewable energy source and to the heterogeneous occupancy schedule. 1.2. Main contributions of the work In this work we propose an EMS for grid-connected MGs, to manage the load supply with the maximum exploitation of solar energy, while at the same time improving the thermal comfort of the microgrid occupants. The proposed methodology adopts a simulation-based approach which iteratively looks for the optimal solution to the underlying optimal control problem. In recent years, simulation-based optimization 3

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methods for energy building control are emerging: these methods use detailed Building Energy Performance Simulation (BEPS) models, developed for example in EnergyPlus, TRNSYS, Modelica, etc., not only for simulation purposes, but also to design optimal EMSs [44, 36]. The advantage of these BEPS models is that they can describe with great realism the interaction between loads, DERs and the occupants’ behaviour. However, due to the large scale and complex nature of the resulting optimization problem, dimensionality issues are faced, and predictive control computations must typically rely on simplified (linear) thermal model to avoid nonlinear non-convex high-dimensional problems, whose solution may require a quite formidable computational burden if online solutions are required [13, 28, 1]. The development of simulation-based optimization methods with the capability of handling large scale EMS instance in buildings or groups of buildings is still a challenging problem. This paper addresses this problem by employing a recently developed algorithm, namely PCAO (Parameterized Cognitive Adaptive Optimization), for energy efficient optimization in microgrids. PCAO is an adaptive optimization algorithm that is capable of efficiently and scalable handling large-scale problems as it has been exhibited in many different applications including large scale traffic control systems, energy efficient buildings and multi-robot teams [20, 33]. A microgrid test case, developed in EnergyPlus, is used to validate the performance of the proposed PCAO energy management strategy. The test case consists of three building that share the energy generated by a solar photovoltaic (PV) panel. The three buildings exhibit heterogeneous occupancy schedules, reflecting the different nature of each building (residential, commercial, industrial). The buildings can also interact with the main grid (buy and sell energy) with different tariffs. The controllable loads consist of a team of heating, ventilation, and air conditioning (HVAC) units, installed in all the thermal zones of the buildings, for a total of twenty thermal zones. By managing the set points and the fan speeds with which each HVAC unit operates, the demand response of the building can be regulated. The energy management problem is to manage the load supply, exploiting at the maximum extent the solar energy coming from the PV panel. The problem is not trivial due to the intermittent behaviour of the solar energy, to the uncertain dynamics of the buildings, to the heterogeneous occupancy schedules, and to the fact that the thermal comfort that must be guaranteed for the microgrid occupants. In fact, the performance criterion to be minimized is a combined criterion that takes into account both the aggregated energy cost and the percentage of people dissatisfied with thermal comfort in the microgrid. To evaluate the potentialities of the PCAO energy management strategy, extensive comparisons with several rule-based and alternative optimization-based EMS strategies are presented. The PCAO strategy exhibits better performance than the rule-based strategies. Furthermore, while attaining slightly better improvements than alternative optimization-based strategies (which employ constrained nonlinear optimization or genetic algorithms), the computational time required by the PCAO strategy is much smaller. Finally, constrained nonlinear-based and genetic-based strategies provide with open-loop set point and fan speed schedules, which are expected to be prone to instability and sensitive to building modelling errors and variable weather conditions. The PCAO strategy, being intrinsically closedloop, can provide with improved robustness to uncertainties in the building model: this claim is supported by simulations showing that the same PCAO feedback controller can attain consistent improvements under different weather conditions (sunny/cloudy weather), while the open-loop strategies obviously need to recalculate their schedule every day. The rest of the paper is organized as follows. In Section II we present the problem formulation and the performance objectives to be optimized. Section III presents the details of the microgrid test case used for the simulations. In Section IV the PCAO optimization algorithm is explained. In Section V simulation results demonstrate the efficiency of the proposed algorithm in dealing with the EMS task.

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2. Problem Formulation In this study we consider grid-connected photovoltaic-equipped microgrids. The buildings of the microgrid share the solar energy of a PV field to satisfy their energy needs. Furthermore, the buildings can interact with the solar panel and the main grid in the following ways: since the PV panel is a renewable energy source that provides power only when the sun is available, the solar energy is a ”must-take” resource always used when it is available. If the solar energy is not enough to satisfy the microgrid energetic needs, then extra energy must be bought from the main grid; on the other side, if the solar energy is in excess with respect to the microgrid energetic needs, then the excess of energy can be sold to the main grid. We assume that the microgrid is heterogeneous, i.e. it comprises different buildings of different nature (residential, commercial, industrial, etc.). The consequences of the heterogeneity of the microgrid are threefold: the buildings have possibly different sizes, a different number of thermal zones and different energetic needs; every building has a different occupancy schedule, and this affects differently the energy demand of each building; since electricity rates typically vary for residential, commercial, and industrial customers, each building buys and sells energy according to a different tariff. In particular, the solar energy from the PV panel is distributed proportionally to the energy demand of each building of the MG (according to the Kirchhoff’s Law): if the solar energy is not enough, each building buys extra energy according to its tariff, while if the solar energy is in excess, each building sells its own excess of energy according to its tariff. The interaction between the microgrid, the PV panel and the main grid is sketched in Fig. 1: in this figure, a Central Control Unit (CCU) collects all the data coming from the grid in terms of energy demands, tariffs, thermal comfort and any other information that might the useful to optimize the aggregated performance of the microgrid (e.g. weather forecasts, occupancy patterns, etc.). The task of the CCU is to implement an efficient EMS with the ability to optimize both the aggregated energy cost and the aggregated thermal comfort of the microgrid.

Figure 1: Interactions inside a grid-connected photovoltaic-equipped microgrid 131 132 133 134 135 136

In order to perform its optimization the EMS balances the supply of electricity on the microgrid with the electrical load, by adjusting the controllable loads of the microgrid: such task is known as load management, or demand side management (DSM). In our problem formulation the following assumptions are made: the microgrid is the owner of the PV field, so that the solar energy is free of charge; the electricity prices do not vary according to the time-of-day; the PV panel is in close proximity to the energy users and distribution losses can be neglected; no storing batteries are available, since these devices are typically very expensive 5

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and with a relatively short life-cycle [22, 15]. Energy storage for microgrids is still a young technology that poses many challenges, however, there is an ongoing research on substituting batteries with new, more efficient techniques [39, 17, 22]. Finally, since the emphasis of the work is on joint optimization of energy cost and thermal comfort, HVACs are the only controllable loads under consideration: this is a simplification based on the fact that HVAC operations account for nearly 50% of the energy consumed by a building and on the observation that other types of loads (lighting, industrial machines, PCs, etc.) are not responsive loads that cannot be curtailed [31]. Thus, the necessary load management is achieved by regulating the set points and the fan speed of the HVACs. The DSM problem can be described as the problem of finding a strategy of the form (sp, f ) = H (Te, Hu, Oc,W f )

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(1)

for the management of the set points (sp) and fan speeds ( f ) of the HVAC units, based on the information gathered from thermal zone temperatures (Te), thermal zone humidities (Hu), occupancy schedule of the thermal zones (Oc), weather conditions and weather forecasts (W f ). By managing the loads for each building #i of the microgrid, the collection of all the functions H in (1) determines the EMS strategy for the entire microgrid.

Figure 2: The demand side management in building #i

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2.1. Performance Index The performance index reflects the system requirements and control specifics of the microgrid. Every realistic performance index must take into account two terms: the energy cost and the thermal comfort of the occupants. The energy cost and the thermal comfort are usually combined in a multiobjective criterion via a weighted summation [38, 45]. At time t the aggregate performance index of a microgrid with N buildings is defined as N

TC(t) = ∑ (k ∗ ESi (t) + (1 − k) ∗CSi (t))

(2)

i=1

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where ESi is the energy score and CSi the thermal comfort score of building #i. According to the importance that the designer wants to give to a term with respect to the other the summation can be weighted using the scaling factor 0 < k < 1. The energy and the comfort score are designed (typically via normalization factors) so as to be of the same order of magnitude and contribute fairly to the total score. By energy cost it is intended the cost that will appear in the electricity bill (in A C): it is logical to suppose that the energy coming from the renewable sources is free, while only the energy absorbed from the main 6

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grid will be paid. Besides, some systems also allow the microgrid to sell to the main grid the energy in excess. Note that, since not all the electrical grids allow to sell energy (or allow it only during peak hours when the global energetic demand is larger, the selling mode can be also intended as a mode during which the MG uses the spare energy for the not responsive loads or uses it to recharge electric vehicles that might be connected to the microgrid. While the energy cost can be univocally define, different methods are available for measuring the thermal comfort. In this work we concentrate on the thermal comfort model developed by Fanger [2], which evaluates the Predicted Percentage of Dissatisfied people (PPD) in a room. Fanger proposed an equation for thermal comfort that relates environmental and physiological factors with the thermal sensation: the equation is fairly complex and it is not of our concern here. The Fanger equation is usually solved numerically; most BEPS simulators directly provide the corresponding PPD Fanger index (in %), using charts and diagrams based on statistical data from which optimal comfort conditions can be read given a knowledge of metabolic rate and clothing insulation.

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3. The Microgrid Test Case

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The microgrid of interest consists of three buildings of different sizes: each building has two floors, covering a surface of 375, 200 and 325 m2 respectively. An EnergyPlus model [10, 9] simulates the complex energetic and thermal behavior of each building. In order to make the EMS tasks more challenging, the three buildings have different use and different occupancy schedules, which are show in Table 1. In particular, the first and the second building are assumed to host commercial (only during the morning) and industrial activities (during the entire day); the third building exhibits a typical residential occupancy schedule, with people being in the building during the morning and around lunch time. It has to be noted that since the emphasis of the work is on demand side management in the presence of solar energy, we neglect the evening and night hours. Table 1: Occupancy Schedule

Building 1 Building 2 Building 3

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No. of Thermal Zones 8 thermal zones 4 thermal zones 8 thermal zones

Occupancy Schedule 8am - 1 pm 6am - 6 pm 8am - 10am and 1pm - 3pm

The schedule of Table 1 has been designed in such a way that a variety of situations occur: all three buildings are occupied (from 8am to 10am), only building 2 is occupied (from 6am to 8am, and from 3pm to 6pm), only building 1 and 2 are occupied, only buildings 2 and 3 are occupied, and so on. Such a heterogeneous occupancy schedule make the EMS tasks very challenging, since the optimization must take into account the users’ behaviour and must intelligently change the load for every building. It is assumed that all the thermal zones of one building exhibit the same occupancy pattern. The EMS consider the problem of operating the HVAC during summer, in order to cool-climate the rooms in an energy efficient manner to a user comfort satisfying level. An HVAC unit is present in each thermal zone the microgrid (for a total of 20 thermal zones). The operation of the each HVAC unit has two manipulable inputs: the first one is the selection of HVAC set points. The operating limits for such set points are between 18-30 degrees Celsius, so that the thermal comfort does not exceed safety levels. The second HVAC manipulable input is the regulation of fan speeds, with operating limits in the range 0-100%. 7

Table 2: Cost Calculation

for t=1:T f for i=1:3 if Qi (t) >= EiPV (t) ESi (t) = pBi ∗ (Qi (t) − EiPV (t)) ∗ f p

(3)

ESi (t) = pSi ∗ (Qi (t) − EiPV (t)) ∗ f p

(4)

else

end CSi (t) = Fi (t) ∗ fc BCi (t) = k ∗ ESi (t) + (1 − k) ∗CSi (t) end TC(t) = BC1 (t) + BC2 (t) + BC3 (t) end

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The calculation of the cost (2) for each building and for the microgrid system is described in Table 2. At each time step, the cost for each building is calculated depending on the available solar energy. If energy required by building #i (Qi ) exceeds the available PV energy for the same building (EiPV ) then, extra-energy from the main grid is bought at price pBi . When the available PV energy exceeds the energy demand of building #i, the building sells the excess of energy to the main grid at price pSi . In order to make the contribution of the energy and the comfort score of similar order of magnitude, in (3) and (4), such scores are multiplied by the scaling factors f p and fc , respectively. In our specific case, the daily energy consumption of the building is of the order of 50-100 kWh, leading to a daily energy cost in the range of [-4, +3] A C (depending on the EMS strategy adopted and on the available solar energy), while the PPD is a percentage from 0 to 100, even if all the tested EMS strategies do not exceed 15%. Taking into account these orders of magnitude we selected f p = 1 and fc = 1/4. The weight factor k in (2) is equal to 0.5, so that energy cost and thermal comfort contribute equally in the total cost. Table 3: Energy Pricing

Building 1 Building 2 Building 3

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Building Category Commercial without VAT Industrial with VAT Residential with VAT

Buying Price [A C/kW h] 0.153 0.175 0.201

Selling Price [A C/kW h] 0.107 0.122 0.140

The electricity prices pBi correspond to real tariffs for residential and industrial/commercial customers (with and without VAT) in the Italian electricity market. Such tariffs have been taken based on the results 8

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collected by the PV Parity project [32], part of the Intelligent Energy Europe programme of the European Commission. The selling electricity prices pSi have been selected 30% smaller than the buying prices, since, as it happens in real-life, the cost of the energy we buy is greater than the cost of the energy we can sell back to the main grid. So, it is more useful to use the solar energy to meet the energy demand, and then eventually sell the spare. The EnergyPlus simulator adopts historical data from summer 2009. The data have been taken from the EnergyPlus website [11] and refer the Italian city of Palermo. The aim was to select consecutive days with fluctuations in solar radiation and temperature, to observe the behavior of each EMS strategy. Thus, 3rd, 4th and 5th of July were selected to conduct our experiments. In Fig. 3, the weather data (solar radiation and temperatures) for the three selected days are presented. There is some weather variability among the three days: the first day, even if it is the coldest one, offers higher amounts of solar radiation. On the other hand, the second day, even if it is warmer, it offers less solar energy, probably due to a cloudy weather.

(a) Solar Evolution per Day

(b) Temperature Evolution per Day

Figure 3: Evolution of Solar Radiation and Temperature during the 3 selected days

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4. The PCAO Algorithm The EMS problem consists in finding an optimal strategy for the HVAC set points and fan speeds such that the combined performance index defined in (2) is minimized. The EMS problem is thus formulated as an optimal control problem aiming at minimizing the index Z Tf

J =

Π(x(t))dt

(5)

0

s.t. x˙ = 228 229 230 231 232 233 234

f (x) + Bu,

B = [0 I]0

(6)

where Π(·) is the analytical expression of the performance index (2), x = [χ 0 υ 0 ]0 contains the thermal state of the building (zone temperatures and humidities) and the HVAC set points and fan speeds. The input u is an augmented input implemented via a pre-integrator υ˙ = u. The function f (x) represents the microgrid dynamics, which are implemented inside the EnergyPlus model, but that are unknown for our purposes. Finally T f is a control horizon over which we have reliable weather forecasts (typically 2-3 days). From an implementation point of view such a control horizon must be intended in a rolling (or reciding) horizon philosophy, i.e., every time step we are looking for the EMS strategy that will minimize the performance 9

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index over a horizon over which we have forecasts. Using dynamic programming arguments, we know that the optimal EMS strategy u∗ satisfies the Hamilton-Jacobi-Bellman (HJB) equation ∗ ∂V (7) min ( f (x) + Bu) + Π(x) u ∂x the difficulty in solving the HJB equation in large-scale systems (like our microgrid) were known to Bellman itself, which coined the term ‘curse-of-dimensionality’ [5]: in order to overcome such difficulties, the PCAO (Parametrized Cognitive Adaptive Optimization) algorithm parametrizes the solution of the HJB equation ∗ (7) as V ∗ (x) = z0 (x)Pz(x) and the optimal EMS strategy via u∗ = − 12 B0 ∂V ∂ x , P is a positive definite matrix and z(·). More details for the function z(·) can be found in [3, 4]: in our specific microgrid case we found that a linear trasformation z(x) = x is sufficient to achieve important improvements (as demonstrated in the section V). With such parametrization, the problem of solving the HJB equation is recast as the problem of finding the matrix P (and thus the EMS strategy u) that better approaches the solution of the HJB equation. The PCAO algorithm defines the close-to-optimality index (mutuated for the principle of optimality [5]) Z k+1 Π(x(t))dt (8) ε(x, P) = min V (x(k + 1)) −V (x(k)) + u

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The solution of the HJB equation (7) brings (8) to zero: implementing a gradient-like descent method Pˆnew = Pˆold − η∇Pˆ ε(x, P),

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η >0

(9)

is not feasible, since, being the microgrid dynamics unknown, an analytic expression for the gradient ∇Pˆ ε is not available.

Figure 4: The PCAO algorithm flowchart for the solution of the EMS problem 249 250 251 252

The PCAO algorithm, whose flowchart is sketched in Fig. 4 updates at every time step the EMS strategy ˆ and to make Pˆ converge as parametrized by Pˆ in an attempt to minimize the close-to-optimality index ε(P) close as possible to the solution of the HJB equation. Fig. 4 reveals the presence of two feedback loops: the primary feedback loop in a real-time one, where actions are applied to the real-world microgrid and 10

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measurements are collected. In parallel with the primary loop, a secondary simulation-based loop interacts with the EnergyPlus model of the microgrid, in order to find better EMS strategies at the next time step. With the term ‘simulation-based’ design we refer to a method where the optimization of the cost function involves an iterative process of system simulation/controller redesign. The simulation-based control design iterative procedure can be summarized as: Step1.

The controller parameters are used to simulate the closed-loop system performance over the whole simulation period. Each simulation period may involve testing/simulating the same controller under different scenarios (different initial conditions and different characteristics for the exogenous factors) so as to make sure that the optimized controller is able to efficiently handle many different possible real-life situations. The optimizer receives the total system performance over the control time horizon.

Step2.

The optimizer calculates the new controller parameters in an attempt to improve the system performance at the next time step. In our case, the optimizer suggests a bank of possible candidate EMS strategies for the next timestep: The PCAO estimator will evaluate the expected (estimated) performance of such candidates and will select the best one for the next time step.

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This iterative procedure is continued over many iterations until convergence of the close-to-optimality index is reached. The interested reader is referred to [19, 3, 4] for an analytical exposition of the stability and convergence properties of the PCAO algorithm. The effectiveness of the proposed method is demonstrated by applying the PCAO algorithm to the microgrid test case and the results are presented in the following section.

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4.1. Feedback Vector

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As expressed by (1), the EMS strategy exploits different information to operate an optimal management: such information is collected in the feedback vector x used to implement the PCAO closed-loop strategy. In particular, every building adopts an EMS strategy which uses information coming from its own thermal zones: the feedback vector of building #i contains:

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• 3 measurements of external weather conditions: outside temperature, outside relative humidity and solar radiation (in [oC], [%] and [W /m2 ]);

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• 6 forecasts for the mean outside temperature over the next 6 hours (in [oC]);

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• 6 forecasts for the mean solar radiation over the next 6 hours (in [W /m2 ]);

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• The n temperatures of the thermal zones, where n is the number of thermal zones shown in Table 1 (in [oC]);

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• The n humidities of the thermal zones (in [%]);

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• A constant term (since the equilibrium of the system is not in the origin).

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• The n set points of the HVAC devices in the thermal zones (in [oC]);

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• The n set points of the HVAC devices in the thermal zones (in [%]);

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• The n signals of occupancy in the thermal zones, from 0=empty to 100=fully occupied (in [%]).

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The choice of the feedback vector has been made according to the following criteria: the zone temperature and humidities are a natural choice for the thermal state of the building; outdoor weather conditions both in the present and the future help to achieve a pro-active control strategy. The information from occupancy is adopted in many smart thermostats available in the market, which typically employ a training period to ”learn” the occupancy schedule and create comfortable conditions some time before people start using the building, according to the so-called ”pre-cooling” strategy. The information about the occupancy of a thermal zone is provided as a state to the linear EMS strategy, rather then as an ”if-then-else” logic condition because it leads to good results and it avoids the implementation of two different EMS strategies (one for the empty and one for the fully occupied situation). With such a choice a unique EMS strategy is calculated for each building: this choice reduces the computational time of the PCAO algorithm. It can be noted how each building collects information relative to its own thermal zones, rather than collecting information coming from all the thermal zones of the microgrid: this choice is also made with the intention to reduce the computational load of the PCAO algorithm. However, it cannot be said that the resulting EMS strategy is decentralized: despite the fact that each building collects information relative to its own thermal zones, the CCU collects the aggregate performance of the microgrid and updates the three management strategies of each building in such a way to optimize the aggregate performance for the whole microgrid. In other words, in each building the function H in (1) uses decentralized information (local state), but the function H itself is updated by the CCU according to a centralized policy (aggregate performance).

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5. Simulation Results

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This section describes the simulation results for the microgrid test case described in Sect. III. The results of the optimization of the demand response via the PCAO algorithm will be exhibited as compared with different classes of EMS strategies. The R2013b version of Matlab, with Energy-Plus 6.1.0 were used. Experiments were conducted in a PC using 16GB of ram and Intel 4770k cpu. For comparison purposes various EMS were implemented and used. In a first comparative study, two Rule Based Controllers(RBC) were adopted. The RBCs employ a simple control strategy, which consists of keeping the HVAC set points of each thermal zone constant to 23oC (RBC1 ) or to 25oC (RBC2 ) and fan speed constant to 30%, during occupancy hours. Such control strategies, yet simple, provide acceptable (but far from optimal) performances in terms of the total score. In the second comparative study, the same RBC set points were used, but with the difference that the so-called ”pre-cooling” strategy was adopted: the HVAC unit are activated one hour before the arrival of occupants. These scenarios will be called as Pre-Cooling Rule Based Controllers (PCRBC). Intuitively, these strategies leads to better PPD scores at the expense of more energy employed: thus, the difference in improvement can be examined as compared with PCAO. As a final comparative study, PCAO is compared with two other optimization-based EMS strategies, based on, fmincon and genetic algorithm, respectively. Comparisons with respect to achieved performance, robustness and convergence speed can thus be examined. Note that each comparative study is performed during the different days presented in Section III, with different weather conditions (Temperature and Solar Radiation). The sum of Energy Cost (in Euros) and the thermal comfort score (in PPD, Predicted Percentage of Dissatisfied) will be used as a measure to compare the performance of each different EMS strategy.

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5.1. Comparison with rule-based EMSs

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Figure 5a presents for each building and for the whole microgrid, revenues and costs for the 3 day experiment. Here, positive values represent the costs in Euros, whereas negative values represent the revenues 12

(a) Cumulative Energy Cost over the 3 days

(b) Mean PPD value over the 3 days

Figure 5: Comparison of Energy Cost and PPD during the 3 selected days

338

in Euros summed up over the 3 days. The percentages in Figure 5b show, for each different building and for the aggregate microgrid) the mean predicted percentage of dissatisfied people over the three days. It can be noted that PCAO achieves a profit of more than 9A C for the whole microgrid, while keeping the PPD at very low levels (around 7%). RBC2 achieves a profit which is very close to the PCAO profit, but at the expense of thermal comfort, which is bigger than 10%. Since the ASHRAE standard suggests that the PPD should be below 10% always during the day, a mean PPD which is bigger than 10% is unacceptable. These two scores (energy cost and thermal comfort) can be translated into improvement in terms of the total cost, as presented in Table 4. PCAO offers a consistent improvement for every day: the improvement varies between 27 and 36 %, as compared to best RBC scenario, which is RBC2 .

339

5.2. Comparison with precooling rule-based EMSs

330 331 332 333 334 335 336 337

340 341 342 343 344

The ”pre-cooling” option can offer improvement in terms of thermal comfort in most EMS strategies. So, it is interesting to compare PCAO with rule-based scenarios that use this strategy (PCRBC). The PCRBC scenarios, although most promising in terms of thermal comfort, are more energetically demand as they require an early activation of HVACs, so as to prepare good thermal comfort conditions when the occupants enter the rooms.



Figure 6: Comparison of Energy Cost and PPD during the 3 selected days 345 346 347

In Figure 6 the PCAO and PCRBC scenarios are compared in the aspect of Energy Cost and PPD. In this case, PCAO performs better both in profits and in thermal comfort. As expected, in comparison with the previous RBC case, the pre-cooling strategy leads to better PPD scores, but using more energy (thus, 13

348 349 350 351

the reduction in revenues). When looking at the total cost, the performance of pre-cooling rule-based EMSs outperforms the performance of the previous rule-based EMSs, but still PCAO is more efficient, as can be seen from the second part of Table 4. The improvements go from 17% to 26% (with respect to PCRBC2 ), depending on the particular day. Table 4: PCAO Improvement (Total Cost) with respect to RBC scenarios and PCRBC scenarios (results validated over the 3 different days of section III)

1st Comparison Day 1 Day 2 Day 3 2nd Comparison Day 1 Day 2 Day 3

352 353 354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375 376

Improvement wrt RBC1 58 % 45 % 49 % Improvement wrt PCRBC1 45 % 35 % 39 %

Improvement wrt RBC2 36% 27% 33% Improvement wrt PCRBC2 26% 17% 24%

5.3. Comparison with optimization-based EMSs Both the RBC and the PCRBC scenarios are simple strategies that do not apply any ”clever” control action in HVACs. In order to compare PCAO with more clever optimization-based EMS strategies, fmincon and ga (from the Matlab Optimization Toolbox) were implemented. Fmincon implements various gradient descent methods, whereas, ga implements the genetic algorithm. As a first attempt, since PCAO looks for a closed-loop EMS strategy parametrized via a matrix P, also fmincon and ga had been implemented in such a way to optimize such a control matrix: however, it has been found that, even after hundreds of thousands of iterations, no effective EMS solutions could be found by these two algorithms. To overcome this problem, a less computationally expensive EMS solution has been adopted, consisting in making fmincon and ga optimize the set points and fan speeds profile every 10 minutes with no feedback information. That is, while in PCAO the set point and fan speed profile is defined via the closed-loop EMS policy, the result of the fmincon and ga optimization is an open-loop profile for the three days. The robustness analysis is not the object of this work, even if, intuitively, a closed-loop control profile is expected to be able to be more robust against different conditions (occupancy schedule, weather conditions, forecast), than open-loop EMS profiles. In this comparative study, apart from the improvements with respect to the energy cost and the thermal comfort, the computational cost of each optimization method plays an important role. Figure 7 demonstrates that PCAO outperforms fmincon and ga in profits, whereas the PCAO thermal comfort is comparable to the fmincon thermal comfort and about 30% better than the ga solution. In Table 5, the results of each optimization method are presented. It is easy to note that only fmincon reaches levels of performance comparable to PCAO, whereas ga is far from those levels. However, both algorithms need enormous amounts of computational time, which translates in many hours-days of experiments. In the first column of Table 5, the improvement with respect to RBC2 is presented, for each day. In the other two columns, the mean number of iterations for each experiment and the corresponding execution time are shown: PCAO accomplishes the energy management task with less iterations and less computational time than the other two methods. 14

Table 5: Comparison between PCAO, Fmincon and Genetic Algorithm

PCAO Fmincon GA

Improvement wrt RBC2 36% - 27% - 33% 33% - 25% - 33% 15% - 13% - 13%

Number of Iterations ∼ 700 ∼ 10000 ∼ 10000


Experiment Time ∼ 20hours ∼ 4days ∼ 4days


Figure 7: Comparison of Energy Cost and PPD during the 3 selected days

377

6. Conclusions

387

This paper proposed a simulation-based optimization approach for the design of energy management systems (EMS) in grid-connected microgrids comprising of buildings of different nature with heterogeneous occupancy patterns. The objective of the EMS was to optimize both energy cost and thermal comfort. Simulation results obtained via a realistic and elaborate EnergyPlus model of a microgrid test case, demonstrate that, despite the fact that the (uncertain) building dynamics, the intermittent nature of the solar energy, and the different occupancy schedules affect the demand response management in a complex manner, the proposed EMS can effectively handle the large-scale and complex nature of the problem. The proposed algorithm intelligently and automatically changes the energy demand of each building according to the occupants’ behaviour. The presented work goes in the direction of enhancing the microgrids with the possibility to be as much independent as possible from the electrical main grid.

388

7. Acknowledgment

378 379 380 381 382 383 384 385 386

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The research leading to these results has been partially funded by the European Commission FP7-ICT2013.3.4, Advanced computing, embedded and control systems, under contract #611538 (LOCAL4GLOBAL).

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